22. Radioactive decay law and carbon dating - half-life time. (4p.)

Question 1

Radioactive decay

Answer 1

Radioactive decay is a random process: each decay is an independent event, and one cannot tell when any particular nucleus will decay. When a given

nucleus decays, it is transformed into another nuclide, which may or may not be radioactive.

The number of nuclei that survive after time t can be obtained with the following formula:

𝑵 = 𝑵𝟎^-𝝀𝒕 , where 𝝀 is the decay constant.

The time required for the number of parent nuclei to fall to 50% of its initial value is called the half-life 𝑇1/2, and may be related to 𝜆 as follows:

𝑇 1/2 = ln2/𝜆

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Question 2

Carbon dating

Answer 2

The radioactive decay of the isotope !” ! 𝐶 , which has a half-life of 5730 years, has been an invaluable aid in determining the age of archeological specimens.

A living organism, such as an animal or a tree, is exchanging CO 2 with the environment, so the ratio of the isotopes in the living organism is the same as it is in the atmosphere. When the organism dies, it ceases this exchange and the relative amount of ! !” 𝐶 decreases by decay. By determining the carbon content of a sample and measuring its activity, one can determine when the organism died. The method is known also as radiometric dating or radiocarbon dating.

Although the 14 | 6 𝐶 concentration varies over long periods, this method can still be used to about 40 000 years.

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